1. Field of the Invention
The present invention relates to methods for readily fabricating three-dimensional photonic crystals.
2. Description of the Related Art
A concept of electromagnetic wave transmission and reflection characteristics being controlled by a structure, which can have a size smaller than the wavelength, has been discussed by Yablonovitch, et al. (Physical Review Letters, 1987, Vol. 58, pp. 2059). According to this document, electromagnetic wave transmission and reflection characteristics can be controlled by periodically arranging structures which can have a size smaller than the wavelength. Light transmission and reflection characteristics can be controlled by decreasing the wavelength of the electromagnetic wave to an order of the light wavelength. Photonic crystals are known for having such a structure, and it is suggested that a reflective mirror, which can have a reflectivity of 100% in a certain wavelength band, i.e., no loss in the light, can be achieved. The concept of no light loss, i.e., achievement of a reflectivity of 100% in a certain wavelength band is called a photonic band-gap, in comparison with an energy gap in a conventional semiconductor. A photonic band-gap for incident light from all the directions can be achieved by structuring a three-dimensional fine periodic structure. Hereinafter, this is referred to as a “complete photonic band-gap”. By the realization of the complete photonic band-gap, various applications, for example, suppression of spontaneous emission in a light-emitting device, are possible and a novel functional device can be realized. However, a functional device, which can have a structure able to realize a complete photonic band-gap in a broader wavelength region, can be useful.
Some structures exhibiting such photonic band-gaps have been discussed before (U.S. Pat. Nos. 6,392,787, 6,597,851, and 5,335,240).
However, a three-dimensional periodic structure exhibiting a photonic band-gap is generally difficult to produce because of its fine structure. Therefore, the three-dimensional periodic structures which can perform in the light wavelength region (the wavelength lower than several μm in vacuum) are rarely produced.
A layer-by-layer structure (LBL structure) that can be produced by stacking layers, which can have a two-dimensional structure, was actually produced and evaluated to experimentally observe a photonic band-gap. For example, a structure discussed in U.S. Pat. No. 6,597,851 and a woodpile structure (FIG. 11) discussed in U.S. Pat. No. 5,335,240 are typical LBL structures.
FIG. 11 is an explanatory diagram of a woodpile structure. The woodpile structure 1000 has a first layer 1001 which is formed by a plurality of rectangular rods which can have a width W and a height H. The rectangular rods of the first layer 1001 extend in the Y-axis direction and are arrayed at a pitch P. The woodpile structure has a second layer 1002 which is formed by a plurality of rectangular rods 1100 which can have the same shape as that of the rectangular rods of the first layer 1001. The rectangular rods of the second layer 1002 extend in the X-axis direction and are arrayed at a pitch P. The woodpile structure has a third layer 1003 which is formed by a plurality of rectangular rods 1100 which can have the same shape as that of the rectangular rods of the first layer 1001. The rectangular rods of the third layer 1003 extend in the Y-axis direction and are arrayed at a pitch P so as to be shifted from the positions of the rectangular rods of the first layer 1001 by a distance of P/2 in the X-axis direction. The woodpile structure has a fourth layer 1004 which is formed by a plurality of rectangular rods 1100 which can have the same shape as that of the rectangular rods of the first layer 1001. The rectangular rods of the fourth layer 1004 extend in the X-axis direction and are arrayed at a pitch P so as to be shifted from the positions of the rectangular rods of the second layer 1002 by a distance of P/2 in the Y-axis direction. The four layers of the first layer 1001 to fourth layer 1004 are stacked in the Z-axis direction to constitute a fundamental period. The woodpile structure 1000 is formed by stacking a plurality of the fundamental periods. FIG. 11 shows a case of that two periods of the fundamental period (1001 to 1004) are stacked. In this structure, all the rectangular rods 1100 are made of a first medium. The portions other than the rectangular rods 1100 are made of a second medium which can have a refractive index different from that of the first medium. The pitch P, width W, and height H of the rectangular rods 1100, the refractive index of the first medium, and the refractive index of the second medium are determined so that the photonic crystal exhibits a photonic band-gap in a desired wavelength region. For example, when the first medium has a refractive index of 3.309, the second medium has a refractive index of 1, and the rectangular rods 1100 have a width W of 0.30×P and a height H of 0.30×P, a complete photonic band-gap is formed in the normalized frequency (angular frequency normalized with a period p) range of 0.362 to 0.432. The photonic band structure is analyzed by a plane-wave expansion method. Therefore, when the rectangular rods 1100 are arrayed at a pitch P of 600 nm, a complete photonic band-gap is formed in the wavelength range of 1389 to 1657 nm.
A variety of methods for fabricating the woodpile structure have been discussed before (U.S. Pat. Nos. 5,406,573 and 5,998,208).
In U.S. Pat. No. 5,406,573, the woodpile structure is fabricated by wafer fusion. In U.S. Pat. No. 5,998,208, the woodpile structure is fabricated by repeating forming of a two-dimensional periodic structure, deposition, and polishing.
The method for fabricating the woodpile which is discussed in U.S. Pat. No. 5,406,573 will be described with reference to FIGS. 12A to 12C. As shown in FIG. 12A, a two-dimensional periodic pattern is formed in a substrate 1201 by etching, and a transfer substrate 1205 comprising a substrate 1204, an etching-stopping layer 1203, and a transfer layer 1202 is fused on the substrate 1201. As shown in FIG. 12B, after the removing of the substrate 1204 and the etching-stopping layer 1203 by etching, a two-dimensional pattern is formed in the remaining transfer layer 1202 by etching. By repeating the fusion, substrate removal, and pattern formation, a laminated structure, which can have a plurality of layers shown in FIG. 12C, is formed.
The method discussed in U.S. Pat. No. 5,998,208 will now be described with reference to FIGS. 13A to 13E. A thin-film layer 1302a made of a first medium is formed on a substrate 1301 by vapor deposition (FIG. 13A), and a two-dimensional periodic pattern is formed in the thin-film layer 1302b by etching (FIG. 13B). Then, the interstices of the two-dimensional periodic pattern formed by the first medium are filled with a second medium 1303a by deposition (FIG. 13C), and the surface is polished (FIG. 13D), resulting in a polished second medium 1303b. A structure shown in FIG. 13E is formed by repeating the thin-film layer formation, two-dimensional periodic pattern formation, deposition, and polishing.
The photonic band-gap is caused by a periodicity of a photonic crystal structure (dielectric constant). In order to produce a photonic crystal structure exhibiting a photonic band-gap in a desired wavelength region, it can be necessary in some circumstances to control a period in the three-dimensional direction (Z-axis direction in FIG. 11). In a fabrication method by stacking layers which have a two-dimensional periodic structure, it can be necessary in some circumstances to control the period of the two-dimensional periodic structure, the dimensional error in each element forming the periodic structure, and the thickness of the layer which can have the two-dimensional periodic structure. In particular, the error in the thickness of the layer, which can have the two-dimensional periodic structure, affects the photonic-band-gap wavelength region more significantly than the error in the dimension of the two-dimensional periodic structure does.
In the woodpile structure shown in FIG. 11, if the actual width W of the rectangular rods 1100 in all the layers is 200 nm when a designed value is 180 nm, the wavelength band of the photonic band-gap shifts by about 60 nm from the designed value. If the actual height (layer thickness) H of the rectangular rods 1100 in all the layers is 200 nm when a designed value is 180 nm, the wavelength band of the photonic band-gap shifts by about 160 nm from the designed value. Thus, the effect of the height error is larger than that of the width error.
In conventional fabrication methods, the error in a fabricated structure is the total of errors during the formation of each layer. Therefore, it can be necessary in some circumstances to control the thickness error of each layer to within 2.5 nm in order to control the shift of the photonic band-gap wavelength from the designed value within 20 nm.
Thus, an acceptable thickness error of each layer can be limited in some cases to a very small range for reducing the shift from a designed value. Therefore, it can be difficult to fabricate three-dimensional photonic crystals that perform in a desired wavelength region.
In the method shown in FIGS. 12A to 12C, errors that occur during the formation of the transfer layer 1202 of the transfer substrate 1205 and errors that occur during the etching for removing the substrate 1204 and the etching-stopping layer 1203 must be controlled within acceptable ranges. In the method shown in FIGS. 13A to 13E, errors that occur during the formation of the thin-film layer 1302a and errors that occur during the polishing must be controlled within acceptable ranges, and also unevenness in the substrate thickness must be controlled within an acceptable range. Thus, the fabrication has been very difficult.